It was the first speech of the local election campaign, so perhaps it is not surprising that David Cameron's claim yesterday that immigration has damaged social cohesion so comprehensively captured the front pages. In its content and its timing it had all the hallmarks of the kind of smooth strategic planning that the Conservative party has often done so effectively but which Downing Street has struggled to reproduce in the past year. The party machine has wrested back control of the political message with predictable results and some collateral damage to the coalition.

Conservatives complain that their critics never allow them a right time to talk about migration. But that is because there is a long history of deploying it as an issue just at the point when the party needs to restore the confidence of its core supporters. And there is no doubt that Mr Cameron has vociferous critics on his own backbenches. The more outspoken ponder openly whether the party leader is really a Conservative at all. And while tracking polls never suggest much support for alternative parties of the right such as the UK Independence party, at last month's Barnsley byelection Ukip beat both of the coalition parties. The start of a local election campaign which will be difficult for the Conservatives and possibly disastrous for the Lib Dems seems too needy a moment for a speech on immigration to be treated as anything more serious than a piece of politicking.

Of course, Mr Cameron is anxious to signal that he understands voters' concerns, that there is something that can be done about them, and that he is doing it. His tone was generally moderate, and it is true that immigration worries people in a way that the last government was slow to appreciate. It is also the case, however, that migration from other EU countries is not something the UK government can directly affect, although making sure that British people have the right skills for whatever jobs are locally available would be one way of reducing the appeal of the UK as a destination. Most migrants last year – two-thirds, according to the Office for National Statistics – came from outside the EU, and they came to work or to study. Many of those who came to work will have taken seasonal jobs, although they have in places (some of which, like North Lincolnshire, have local elections in three weeks' time) put very heavy burdens on community infrastructure. That makes it even more curious that the government has cut the cash for the migration impacts fund that Labour introduced and abandoned the citizenship survey which sought to monitor the impact of new migrants. And the axe – curiously, since in his speech Mr Cameron also complained that not enough migrants speak English – has fallen too on the budget for English language teaching. But most importantly, neither immigration nor ethnicity is the primary predictor of a lack of social cohesion. Instead, as the most recent research has shown, it is the level of economic deprivation. Neighbourliness and extreme poverty tend not to go together.

Meanwhile, Mr Cameron appeared to be playing fast and loose with the coalition agreement. That was certainly what the business secretary, Vince Cable, thought. It is true that the half page of the agreement in which migration appears avoids all mention of targets. That has not prevented the government making a clear commitment to halve net migration to 100,000 in this parliament. Mr Cable argued strongly against limiting highly skilled workers and the graduate students who make such a large contribution to university budgets, but he won only a partial victory. That may explain his initial denunciation of Mr Cameron for inflaming extremism, and his subsequent recantation. The next three weeks will be a severe test as the parties establish the load-bearing capacity of a coalition in an election. Expect more of the same.